Non-Douglas–Kazakov phase transition of two-dimensional generalized Yang–Mills theories

Abstract

In two-dimensional Yang–Mills and generalized Yang–Mills theories for large gauge groups, there is a dominant representation determining the thermodynamic limit of the system. This representation is characterized by a density, the value of which should everywhere be between zero and one. This density itself is determined by means of a saddle-point analysis. For some values of the parameter space, this density exceeds one in some places. So one should modify it to obtain an acceptable density. This leads to the well-known Douglas–Kazakov phase transition. In generalized Yang–Mills theories, there are also regions in the parameter space where somewhere this density becomes negative. Here too, one should modify the density so that it remains nonnegative. This leads to another phase transition, different from the Douglas–Kazakov one. Here the general structure of this phase transition is studied, and it is shown that the order of this transition is typically three. Using carefully-chosen parameters, however, it is possible to construct models with the order of the phase transition not equal to three. A class of these non-typical models is also studied.